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Refernces in the PLD

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Robin Clark 2010-08-13 19:33:08 +01:00
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.gitignore vendored
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@ -13,3 +13,6 @@
*.toc *.toc
*.*~ *.*~
*paper.tex
*.txt

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logic_diagram/Makefile
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@ -16,3 +16,7 @@ paper: paper.tex logic_diagram_paper.tex
# #
logic_diagram_paper.tex: logic_diagram.tex logic_diagram_paper.tex: logic_diagram.tex
cat logic_diagram.tex | sed 's/logic_diagram\///' > logic_diagram_paper.tex cat logic_diagram.tex | sed 's/logic_diagram\///' > logic_diagram_paper.tex
bib: logic_diagram_paper.tex
bibtex paper

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logic_diagram/logic_diagram.tex
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@ -7,7 +7,7 @@ Propositial Logic Diagrams (PLD) have been designed to provide an intuitive meth
a specific sub-set of logic equations, to express fault modes in Mechanical and Electronic Systems. a specific sub-set of logic equations, to express fault modes in Mechanical and Electronic Systems.
PLDs are a variant of constraint diagrams. Contours used to express PLDs are a variant of constraint diagrams. Contours used to express
sets represent failure modes and the Symptomatically merged groups sets represent failure modes and the Symptomatically merged groups
are akin to the `spiders' of constraint diagrams\ref{constraint}. are akin to the `spiders'\cite{howse:rwsd} of constraint diagrams\cite{gil:tafocd}.
%To aid hierarchical stages of fault analysis, it has been specifically developed for the purpose of %To aid hierarchical stages of fault analysis, it has been specifically developed for the purpose of
%joining conjunctive conditions with disjuctive conditions %joining conjunctive conditions with disjuctive conditions
%to group the effects of failure modes. %to group the effects of failure modes.
@ -19,7 +19,7 @@ Nearly all modern safety critical systems involve these three disiplines.
% %
It is intended to be used for analysis of automated safety critical systems. It is intended to be used for analysis of automated safety critical systems.
Many types of safety critical systems now legally Many types of safety critical systems now legally
require fault mode effects analysis\cite{FMEA}, require fault mode effects analysis\cite{sccs}[pp 38-39],
but few formal systems exist and wide-spread take-up is but few formal systems exist and wide-spread take-up is
not yet the norm.\cite{takeup}. not yet the norm.\cite{takeup}.
% %
@ -39,7 +39,7 @@ Propositial Logic Diagrams (PLD) have been designed to provide an intuitive meth
a specific sub-set of logic equations, to express fault modes in Mechanical and Electronic Systems. a specific sub-set of logic equations, to express fault modes in Mechanical and Electronic Systems.
PLDs are a variant of constraint diagrams. Contours used to express PLDs are a variant of constraint diagrams. Contours used to express
sets represent failure modes and the Symptomatically merged groups sets represent failure modes and the Symptomatically merged groups
are akin to the `spiders' of constraint diagrams\ref{constraint}. are akin to the `spiders'\cite{howse:rwsd} of constraint diagrams\cite{gil:tafocd}.
%To aid hierarchical stages of fault analysis, it has been specifically developed for the purpose of %To aid hierarchical stages of fault analysis, it has been specifically developed for the purpose of
%joining conjunctive conditions with disjuctive conditions %joining conjunctive conditions with disjuctive conditions
%to group the effects of failure modes. %to group the effects of failure modes.
@ -51,9 +51,9 @@ Nearly all modern safety critical systems involve these three disiplines.
% %
It is intended to be used for analysis of automated safety critical systems. It is intended to be used for analysis of automated safety critical systems.
Many types of safety critical systems now legally Many types of safety critical systems now legally
require fault mode effects analysis\cite{FMEA}, require fault mode effects analysis\cite{sccs}[pp 38-39],
but few formal systems exist and wide-spread take-up is but few formal systems exist to assist in this, and wide-spread take-up is
not yet the norm.\cite{takeup}. not yet the norm.\cite{sccs}[pp 304-305].
% %
Because of its visual nature, it is easy to manipulate and model Because of its visual nature, it is easy to manipulate and model
complicated conditions that can lead to dangerous failures in complicated conditions that can lead to dangerous failures in
@ -87,7 +87,7 @@ for the analysis of safety critical software and hardware systems.
} }
Propositional Logic Diagrams (PLDs) have been created Propositional Logic Diagrams (PLDs) have been created
to collect and simplfy fault~modes in safety critical systems undergoing to collect and simplfy fault~modes in safety critical systems undergoing
static analysis\cite{FMEA}\cite{SIL}. static analysis.%\cite{sccs}\cite{en61508}.
% %
This type of analysis treats failure modes within a system as logical This type of analysis treats failure modes within a system as logical
states. states.
@ -155,6 +155,8 @@ Definitions of concrete and abstract PLD's follow.
Well-formedness conditions for PLD's are separated from this definition, because of Well-formedness conditions for PLD's are separated from this definition, because of
practical differences between the way they are used to represent software as opposed to practical differences between the way they are used to represent software as opposed to
representing electronics and mechanical systems. representing electronics and mechanical systems.
The concrete definitions for PLD's and Spider Diagrams\cite{howse:sd} share many common features.
\subsection{Concrete PLD Definition} \subsection{Concrete PLD Definition}
@ -362,7 +364,7 @@ $fmg$ in the diagram, where an SMG is a non empty set of test points
$$ \mathcal{G}:SMG \rightarrow P_{fmg} $$ $$ \mathcal{G}:SMG \rightarrow P_{fmg} $$
The logic equation representing an SMG $p_{fmg}$ can be determined thus. The logic equation (using $oplus$ to represent exclusive-or) representing an SMG $p_{fmg}$ can be determined thus.
$$\mathcal{G}_{fmg}(fmg) = \bigoplus_{t \in fmg} (\; \mathcal{F}_{t} (t) \;) $$ $$\mathcal{G}_{fmg}(fmg) = \bigoplus_{t \in fmg} (\; \mathcal{F}_{t} (t) \;) $$
} }
@ -621,7 +623,7 @@ by the FMMD software tool.
Very often a failure mode can only occur Very often a failure mode can only occur
given a separate environmental condition. given a separate environmental condition.
In Fault Tree Analysis (FTA) this is represented by an inhibit gate.\cite{FTA}[pp41-42],\cite{NUK} In Fault Tree Analysis (FTA) this is represented by an inhibit gate.\cite{nasafta}[pp41-42],\cite{nucfta}
\begin{figure}[h] \begin{figure}[h]
\centering \centering
@ -641,17 +643,17 @@ The diagram \ref{fig:inhibit} has a test case in the contour $C$.
Contour $C$ is \textbf{enclosed} by contour $A$. This says Contour $C$ is \textbf{enclosed} by contour $A$. This says
that for failure~mode $C$ to occur failure mode $A$ that for failure~mode $C$ to occur failure mode $A$
must have occurred. must have occurred.
A well known example of this is the space shuttle `O' ring failure that A famous example of this is the space shuttle `O' ring failure that
caused the 1986 Challenger disaster\cite{wdycwopt}. caused the 1986 Challenger disaster\cite{wdycwopt}.
For the failure mode to occur, the ambient temperature had to For the failure mode to occur, the ambient temperature had to
be below a critical value. be below a critical value.
If we take the failure mode of the `O' ring to be $C$ If we take the failure mode of the `O' ring to be $C$
and the temperature below critical to be $A$, we can see that and the temperature below critical to be $A$, we can see that
the low temperature failure~mode $C$ can only occur if $A$ is true. the low temperature failure~mode $C$ can only occur if $A$ is true.
The `O' ring could fail in a different way independant of the critical temperature and this is The `O' ring could fail in a different way independent of the critical temperature and this is
represented, for the sake of this example, by contour $D$. represented, for the sake of this example, by contour $D$.
In terms of propositional logic, the inhibit gate of FTA, and the contour enclosure In terms of propositional logic, the inhibit gate of FTAi\cite{nasafta}[pp 41-42], and the contour enclosure
of PLD represent {\em implication}. of PLD represent {\em implication}.
\\ \\
% \tiny % \tiny
@ -777,7 +779,7 @@ it will not lead to a dangerous failure~mode of the subsystem.
% F & F & T \\ \hline % F & F & T \\ \hline
% F & T & T \\ \hline % F & T & T \\ \hline
% T & F & F \\ \hline % T & F & F \\ \hline
% T & T & T \\ \hline \hline % T & T & T \\ \hline \hline:
% \end{tabular} % \end{tabular}
% %\vspace{0.3cm} % %\vspace{0.3cm}
% \normalsize % \normalsize
@ -908,6 +910,14 @@ The test case AFE represents the condition where all four engines have failed.
%\begin{verbatim} %\begin{verbatim}
%CVS Revision Identity $Id: logic_diagram.tex,v 1.17 2010/01/06 13:41:32 robin Exp $ %CVS Revision Identity $Id: logic_diagram.tex,v 1.17 2010/01/06 13:41:32 robin Exp $
%\end{verbatim} %\end{verbatim}
%\ifthenelse {\boolean{paper}}
%{
% \bibliographystyle{plain}
% \bibliography{../vmgbibliography,../mybib}
%
%}
%{
%}
Compiled last \today Compiled last \today
%\end{document} %\end{document}